Is there a novel Einstein–Gauss–Bonnet theory in four dimensions?
European Physical Journal C
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No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic D>4D>4 dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to D=4D=4. Therefore, the recently introduced four-dimensional, novel, Einstein–Gauss–Bonnet theory does not admit an intrinsically four-dimensional definition, in terms of metric only, as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain D>4D>4 dimensional. As there is no canonical choice of 4 spacetime dimensions out of D dimensions for generic metrics, the theory is not well defined in four dimensions.